A robust statistically based approach to estimating the probability of contamination occurring between sampling locations

Transcription

1 A robust statistically based approach to estimating the probability of contamination occurring between sampling locations Peter Beck Principal Environmental Scientist Image placeholder Image placeholder Image placeholder

2 Current Site Assessment Approach Select Target Size and Design Pattern Site History Judgment Based Decision Statistical Evaluation of Concentration Data Collect data on site history to identify sources of impact Collect target samples at locations of concern Select target shape and size of concern and design a sampling pattern to establish absence at 95% confidence using an unbiased sampling pattern Assess unbiased concentration data using uni-variant statistical tools Interpret the results from the two separate approaches to assess contaminant distribution and site condition

3 The Trouble with the Hot Spot Group trial in data interpretation Participants selected sample locations Doted line represents actual hot spot Solid line represents linear based interpolation Dashed line represents nearest clean sample interpretation Note the high degree of variability and uncertainty

4 What Does the Hot Spot Mean

5 Frequency Lead Histogram Consistent Scale Frequency Cumulative % % % Interpreting Concentration Data Lead Consistent Bin Range 80.00% 60.00% % % 0.00% Bin

6 Frequency Lead Histogram Variable Scale % Frequency Cumulative % % Interpreting Concentration Data Lead Variable Bin Range 80.00% 60.00% Bin % 20.00%.00%

7 Limitations of Uni-variate statistics Assumes samples were collected in an un-biased manner Dissociates location and concentration (ie. No relationship between the two) Ignores sample location as a factor Normal and Log-Normal distribution not applicable in many situations Log-Normal distribution can be unstable Non-parametric methods overcome distribution issues but still do not consider location Can not provide confidence in spatial data interpretation

8 Why is Spatial Relationship Important

9 Spatial Geostatistics Based on approach used in the mining industry Allows for spatial relationship between the samples Unaffected by sample biased The VARIOGRAM or SEMIVARIOGRAM is the fundamental Assessment Tool. The variogram present random variance, spatial variance as well as the range of influence of samples Data evaluation is done by Kriging Probability plots developed by Indicator Kriging

10 The Variogram h 1 2 n n i 1 [ X i X 2 i h]

11 One Dimensional Example Distance Spatial h=1 (X i -X i+h ) 2 =(1-2) 2 =1 (X i -X i+h ) 2 =(2-3) 2 =1 (X i -X i+h ) 2 =(9-10) 2 =1 n=9 h 1 2 n i n [ X i X h=2 (X i -X i+h ) 2 =(1-3) 2 =4 (X i -X i+h ) 2 =(2-4) 2 =4 (X i -X i+h ) 2 =(8-10) 2 =4 n=8 2 i h]

12 Variogram Types and Examples

13 Kriging and Indicator Kriging Kriging Mathematical technique for assigning best linear moving average concentration over a defined area. Considered the best method of estimating concentration distribution because: Avoids systematic bias Minimises the error of estimation (kriging error) Requires development and data input from variogram Indicator Kriging Assign a value of 1 to clean samples and a value of 0 to dirty samples Results in a Probability Plot of presence and absence of contamintion

14 So Why Consider Spatial Geostatistics Provides a linkage between concentration, variance (micro + macro) and location Separates random and spatial components of variance Micro-scale (sample scale) variance always in Nugget Effect (random variance) Macro-scale (spatial variance) is either spatially related, random (Nugget Effect) or a combination of the two Assist in establishing when sufficient samples have been collected to characterise a site Provides a robust method for predicting uncertainty in impact distribution, remediation volumes and cost.

15 Case Study 1: Application to 19ha Parkland Parkland and Sporting Ovals in Armidale NSW. Impact by fill from gasworks site was suspected. Investigations commenced in 2000, with a limited sampling program and initial results were used to inform a staged geostatistical assessment process

16 Initial Assessment Stage Results Variogram for PAH concentration. The results were used to develop confidence regions for the initial assessment area using indicator Kriging and then selecting additional sampling locations

17 Second Assessment Stage Variogram for PAH concentration. The results were used to revise confidence regions for the second stage assessment area using indicator Kriging and then selecting additional sampling locations

18 Third Assessment Stage Note there was little change in variogram between stage 2 and 3 sampling. Thus further sampling would offer limited benefit

19 Final Results

20 More Recent Advances Effects of different approaches and skill in the development of the variogram on the reliability of spatial interpretation is an important consideration Using different variograms and assessing the effects on interpretation can assist in clarifying the reliability of the spatial interpretation Utilising only primary sample results can lead to overestimation of statistical confidence and in the case of spatial geostatistics, over estimation of the confidence in the spatial interpretation The QA/QC data collected can be utilised to factor in sample scale variance often caused by heterogeneity Inclusion of the blind duplicate and split samples allows incorporation of the sample scale variance into the variogram development and accounts for it in the spatial interpretation

21 Case Study 2: Effects of Variogram and Variance A 2ha site was intensively assessed to facilitate in-situ waste classification A total of 303 primary samples were analysed, with 108 (~36%) samples analysed exceeded adopted criteria for one or more contaminants The effects of different variogram interpretation was assessed by development of variogram by different assessors with different time budgets Lead QA/QC data was used to assess the effect of random variance on the variogram and confidence mapping

22 Variogram Variogram Variogram Variograms Cd Data Column D: Cadmium Direction: 0.0 Tolerance: Cadmium data was assessed for spatial relationship and variance Effects of variations in various aspects of the variogram on the data interpretation were examined, including: Increasing variance Reducing random variance Decreasing the lag distance and range of influence Using a different model Lag Distance Column D: Cadmium Direction: 0.0 Tolerance: 40.0 Key Variogram Data Transformed: None Sill: 700 Nugget: 50 Range: 35 Model: Spherical Key Variogram Data Transformed: None Sill: 800 Nugget: 1 Range: 35 Model: Spherical Lag Distance Column D: Cadmium Direction: 0.0 Tolerance: Key Variogram Data Transformed None Sill: 770 Nugget: 1 Range: 15 Model: Gaussian Lag Distance

23 Variogram Variogram Variogram Variograms Pb Data Column G: Lead Direction: 0.0 Tolerance: Lead data was assessed for spatial relationship and variance Effects of variations in various aspects of the variogram on the data interpretation were examined, including: Reducing random variance Decreasing the lag distance and range of influence Log Transforming the data before variogram development Key Variogram Data Transformed None Sill: Nugget: 1 Range: 17 Model: Rational Quadratic Lag Distance Column D: Lead Log Direction: Tolerance: 20.0 Key Variogram Data Transformed Log Sill: 2.5 Nugget: 0.25 Range: 25 Model: Rational Quadratic Lag Distance Column D: Lead Log Direction: Tolerance: Key Variogram Data Transformed Log Sill: 2.5 Nugget: 0.25 Range: 20 Model: Rational Quadratic Lag Distance

24 Comparison of Results Cd Pb

25 Variogram Variogram Inclusion of QA/QC Samples Lead Data The variogram shows that the overall random variance component increased from <1% to about 10% Column G: Lead Direction: 0.0 Tolerance: Column D: Lead Direction: 0.0 Tolerance: Primary Data Only Primary Blind Duplicate and Split Data Only Lag Distance Lag Distance

26 Confidence Mapping

27 Adjusting Indicator Krige Assigning 0 or 1 to samples is deterministic and does not take into account measurement uncertainty Using a probabilistic approach to assigning the indicator krige value can take this measurement uncertainty into account. 0 C+U Decision Criteria C 1 C-U Uncontaminated Uncontaminated Contaminated Contaminated Contaminated Deterministic Approach Uncontaminated Possibly Contaminated Maybe Contaminated Probably Contaminated Contaminated Probabilistic Approach

28 Variogram Results of Robust Statistical Assessment Legend Concentration 5 to to to to to to to Indicator Krig Value Variogram Column C: Zinc (mg/kg) Direction: 5.0 Tolerance: to to to to Probability Distribution Lag Distance

29 Conclusions Current site characterisation practice collects spatially distributed data, interpretation of the extent of impact and uncertainty is generally based on judgment Uni and Bi-variant statistical tools are available to assess uncertainty Uni-variant approaches generally rely on the assumption of random distribution and unbiased sample collection, which is rarely met Bi-variant variant approaches link concentration, variance and location thus allowing estimation of the random and spatial component of variance allowing development of probability distributions on the presence or absence of contamination Results are generally robust even when variograms utilised are diverse Inclusion of QA/QC samples in the variogram development results in more realistic probability distributions

30 Presentation title